The (D) Property in Banach Spaces


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Soybas D.

ABSTRACT AND APPLIED ANALYSIS, 2012 (SCI İndekslerine Giren Dergi) identifier identifier

  • Basım Tarihi: 2012
  • Doi Numarası: 10.1155/2012/754531
  • Dergi Adı: ABSTRACT AND APPLIED ANALYSIS

Özet

A Banach space E is said to have (D) property if every bounded linear operator T : F -> E* is weakly compact for every Banach space F whose dual does not contain an isomorphic copy of l(infinity). Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V*) property of Pelczynski (and hence every Banach space with (V) property) has (D) property. We show that the space L-1(v) of real functions, which are integrable with respect to a measure v with values in a Banach space X, has (D) property. We give some other results concerning Banach spaces with (D) property.